The study focuses on interaction of a "strong" adsorbate with an ice surface. Ammonia adsorption on an ice cluster (H2O)(293) is investigated by Monte Carlo simulations, as a function of coverage at T = 110 K. At low coverages, ammonia is attached to dangling H-atoms on the surface, while forming additional weaker bonds with neighboring dangling O. At high coverages insertion is observed of the NH3 molecules into the surface. The process is driven by the ability of NH3 molecules to cleave strained H2O ... H2O hydrogen bonds in the ice surface, and to form strong N ... HO bonds with the water molecules.